ECIV 720 A Advanced Structural Mechanics and Analysis

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ECIV 720 A Advanced Structural Mechanics and
Analysis

• Non-Linear Problems in Solid and Structural
  Mechanics
• Special Topics

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Introduction
Nonlinear Behavior Response is not directly
proportional to the action that produces it.
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Introduction
Recall Assumptions

• Small Deformations
• Linear Elastic Behavior

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Introduction
Linear Behavior
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Introduction
A. Small Displacements
Inegrations over undeformed volume
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Introduction
B. Linear Elastic Material
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Introduction
C. Boundary Conditions do not change (Implied
Assumption)
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Introduction
If any of the assumptions is NOT satisfied
NONLINEARITIES
Geometric Assumption A or C not satisfied
Material Assumption B not satisfied
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Classification of Nonlinear Analysis
Small Displacements, small rotations Nonlinear
stress-strain relation
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Classification of Nonlinear Analysis
Large Displacements, large rotations and small
strains Linear or nonlinear material behavior
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Classification of Nonlinear Analysis
Large Displacements, large rotations and large
strains Linear or nonlinear material behavior
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Classification of Nonlinear Analysis
Change in Boundary Condition
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Classification of Nonlinear Analysis
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Nonlinear Analysis
Cannot immediately solve for d
Iterative Process Required to obtain d so that
equilibrium is satisfied
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Solution Methods
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Newton-Raphson
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Newton Raphson
With initial conditions
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Modified Newton-Raphson